A furniture trader deals in only two items — chairs and tables. He has Rs. 50,000 to invest and a space to store at most 35 items. A chair costs him Rs. 1000 and a table costs him Rs. 2000. The trader earns a profit of Rs. 150 and Rs. 250 on a chair and a table, respectively. Formulate the above problem as an LPP to maximise the profit and solve it graphically.
Answer: Max Z = Rs 6750 at (20, 15): 20 chairs and 15 tables
Solution
Let the trader buy x chairs and y tables. Profit to maximise: Z=150x+250y. Storage: x+y≤35 Investment: 1000x+2000y≤50000⟹x+2y≤50 x≥0,y≥0 The corner points of the feasible region are obtained by intersecting the boundary lines; x+y=35 and x+2y=50 meet at (20,15). Evaluate Z=150x+250y: (0,0): Z=0 (35,0): Z=5250 (20,15): Z=3000+3750=6750 ← maximum (0,25): Z=6250
∴Zmax=Rs 6750 at (20,15)
The trader should stock 20 chairs and 15 tables for a maximum profit of Rs 6750.Feasible region for the chairs and tables LPP, with corner points A(0, 25), B(20, 15) and C(35, 0).
